You are to make monthly deposits of $475 into a retirement account that pays 10.

Question

You are to make monthly deposits of $475 into a retirement account that pays 10.8 percent interest compounded monthly.

If your first deposit will be made one month from now, how large will your retirement account be in 33 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

If your first deposit will be made one month from now, how large will your retirement account be in 33 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

S = R{[(1 + i)n -1]/i}      

S is future value, R is periodic payment, i is interest rate per period, n is number of periods

Here R = 475, i = 10.8/12(100) = 0.9/100 = 0.009 (since compounded monthly)

n = 33*12 = 396

==> S = (475){[(1 + 0.009)396 -1]/0.009}     

==> S = (475){[(1.009)396 -1]/0.009}

==> S = 475(3749.529016)

==> S = $ 1781026.283

Therefore Retirement account value = $1781026.28

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